Incorporating A Research Problem In A Numerical Methods Course For Mechanical Engineers

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Incorporating A Research Problem In A Numerical
Methods Course For Mechanical Engineers

• Autar Kaw
• Department of Mechanical Engineering
• University of South Florida
• http//numericalmethods.eng.usf.edu

Sponsored by National Science Foundation
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Why incorporate real-life problems and research?

• Train students in state-of-the-art research in
  emerging technologies.
• Real world application of course work increase
  comprehension.
• Encourage that education and research are of
  equal value and are complementary parts of an
  integrative engineering and science education
  enterprise.

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BRIDGEof LIONS (1927)
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Bascule Bridge THG
Hub
Trunnion
Girder
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Trunnion-Hub-Girder Assembly Procedure
Step1. Trunnion immersed in dry-ice/alcohol Step2.
Trunnion warm-up in hub Step3. Trunnion-Hub
immersed in dry-ice/alcohol Step4. Trunnion-Hub
warm-up into girder
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Trunnion Stuck in Venetian Causeway Bridge

• When the trunnion was inserted into the hub, the
  trunnion got stuck before it could be fully
  inserted.

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Consultant Calculations
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Thermal Expansion Coefficient Variation with
Temperature
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Estimating Contraction Accurately
Change in diameter (?D) by cooling it in dry
ice/alcohol is given by

• Solve the problem using Trapezoidal Rule for
  discrete data.
• Solve the problem by using regression to find an
  expression for thermal expansion coefficient.
• Regression models require solution of
  simultaneous linear equations.

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Other numerical methods problems

• What fluid temperature will give the desired
  contraction results in a nonlinear equation?
• How much time would it take to cool the trunnion
  needs solution of an ordinary differential
  equation.
• Differentiation quantitatively shows how lower
  the temperature, lower the contraction per unit
  temperature.

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A Lesson on Significant Digits
Observed Data
Default Format in Excel for Regression
Scientific Format in Excel for Regression
µin/in/oF
T -300oF
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Quantitative Survey Results
7-Truly outstanding, 6-Excellent, 5-Very Good,
4-Good, 3-Adequate, 2-Poor, 1-Truly Inadequate
Based on 52 Responses
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Quantitative Survey Results
For all questions, approximately 90 of the
students responded with Good or better
evaluations.
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Recurring Themes in the Qualitative Survey
Questions

• What did you like most about the problem-centered
  approach? (51 Responses)
• Application of course material to real-life
  engineering problem (20)
• Application of different solution approaches to
  the same problem and comparing the quality of the
  solutions (9)
• What did you like least about the
  problem-centered approach? (49 Responses)
• Significant number of students had no criticism
  (12)
• Working on one problem throughout the semester
  was monotonous (19)
• What would you like to change about the
  problem-centered approach? (48 Responses)
• Significant number of students mentioned no
  changes (15)
• Increase the number of examples (21)

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Conclusions

• A single real-life problem was successfully
  implemented in a course in Numerical Methods.
• The breadth of topics covered included all topics
  of a typical Numerical Methods
• Students found incorporating the research problem
  created a better learning environment in learning
  the fundamentals of the course.